FINUDA hypernuclear spectroscopy

Nuclear Physics A 835 (2010) 414–417 www.elsevier.com/locate/nuclphysa

FINUDA hypernuclear spectroscopy M. Agnello a,b , L. Benussic , M. Bertanic , H.C. Bhangd , G. Bonomie, f , E. Bottag,b , M. Breganth,i , T. Bressanig,b , S. Bufalinog,b , L. Busso j,b , D. Calvob , P. Camerinih,i , B. Dalenak,l , F. De Morig,b , G. D’Erasmok,l , F.L. Fabbric , A. Feliciellob , A. Filippib , E.M. Fiorek,l , A. Fontana f , H. Fujiokam , P. Genova f , P. Gianottic , N. Grioni , B. Kangd , V. Lucherinic , S. Marcellob,g1 , F. Moiae, f , T. Marutan , N. Mirfakhraio , P. Montagna f,p , O. Morraq,b , T. Nagaem , D. Nakajimar , H. Outa s , A. Pantaleol , V. Paticchiol , S. Pianoi , R. Ruih,i , G. Simonettik,l , A. Toyodat , R. Wheadonb , A. Zenonie, f a

t

Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy b INFN Sezione di Torino, via P. Giuria 1, Torino, Italy c Laboratori Nazionali di Frascati dell’INFN, via. E. Fermi, 40, Frascati, Italy d Department of Physics, Seoul National University, 151-742 Seoul, South Korea e Dipartimento di Meccanica, Universit` a di Brescia, via Valotti 9, Brescia, Italy f INFN Sezione di Pavia, via Bassi 6, Pavia, Italy g Dipartimento di Fisica Sperimentale, Universit` a di Torino, Via P. Giuria 1, Torino, Italy h Dipartimento di Fisica, Universit` a di Trieste, via Valerio 2, Trieste, Italy i INFN Sezione di Trieste, via Valerio 2, Trieste, Italy j Dipartimento di Fisica Generale, Universit` a di Torino, Via P. Giuria 1, Torino, Italy k Dipartimento di Fisica Universit` a di Bari, via Amendola 173, Bari, Italy l INFN Sezione di Bari, via Amendola 173, Bari, Italy m Department of Physics, Kyoto University, Sakyo-ku, Kyoto Japan n Department of Physics, Tohoku University, Sendai 980-8578, Japan o Department of Physics, Shahid Behesty University, 19834 Teheran, Iran p Dipartimento di Fisica Nucleare e Teorica, Universit` a di Pavia, via Bassi 6, Pavia, Italy q INAF-IFSI, Sezione di Torino, corso Fiume 4, Torino, Italy r Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan s RIKEN, Wako, Saitama 351-0198, Japan High Energy Accelerator Research Organization (KEK), Tsukuba,Ibaraki 305-0801, Japan

Abstract The FINUDA experiment collected data to study the hypernuclear production on different targets, that is 6 Li, 7 Li, 9 Be, 12 C, 13 C, D2 O, 27 Al and 51 V. The hypernuclei formation was achieved − + A Z → ΛA Z + π− . From the study of the outthrough the strangeness-exchange reaction K stop − coming π , information about the hypernuclei binding energies and capture rates can be deduced. Such results for the following nuclei 7 Li, 9 Be, 13 C and D2 O will be presented. Key words: hypernuclei, hypernuclear spectroscopy 1. Introduction FINUDA is a hypernuclear physics experiment, the first to take place at a collider, that used the DAΦNE Φ Factory machine of the “Laboratori Nazionali di Frascati” of INFN. Details about 1 On

sabbatical leave at Kyoto University, Kyoto, Japan, under JSPS Program

0375-9474/$ – see front matter Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2010.01.232

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the experiment can be found elsewhere [1]. The specific aim of FINUDA was to study production and decay of Λ-hypernuclei by stopping, in thin targets (0.1-0.2 g/cm2 ), the negative kaons − +A Z →ΛA Z + π− , originating from the Φ decay through the strangeness-exchange reaction K stop A A where Z indicates the target nucleus and Λ Z the Λ hypernucleus in which a Λ particle replaced a neutron. FINUDA unconventional and innovative apparatus allowed the positioning of 8 different target modules around the interaction region. In this way different elements could be studied contemporaneously, with the same apparatus and with the same analysis technique, allowing for a direct comparison between distinct materials. During two data taking (2003/04 and 2006/07) FINUDA could study the production of Λ-hypernuclei on 6 Li, 7 Li, 9 Be, 12 C, 13 C, D2 O, 27 Al and 51 V. The results about hypernuclear spectroscopy for the following nuclei 7 Li, 9 Be, 13 C and D2 O, collected during the latest data taking will be presented. 2. Data analysis The raw π− momentum distribution related to high quality negative tracks emerging from the target under study in coincidence with a K − stop is shown in the insets of Fig. 1 in a 0.5 MeV/c per bin distribution. Clear peaks for 7 Li, 13 C and D2 O and a bump in the region [280-285] MeV/c for 9 Be can be noticed. They are the signature of the presence of Λ-hypernuclei. Measuring the pion momentum with the experimental apparatus and considering the energy and the momentum − conservation laws for the reaction K stop +A Z →ΛA Z + π− , one can get the hypernucleus mass in the specific level:  mHyp,i =

(mK − + mA Z − Eπ,i )2 − p2π,i

where mK − is the K − mass, mA Z is the target nucleus mass for the ground state, mHyp,i the mass of the particular ΛA Z hypernucleus formed in the ith energy level state, pπ,i is the pion momentum for the produced hypernucleus level and Eπ,i the corresponding pion total energy. Knowing this mass, it is possible to calculate the Λ binding energy BΛ,i , that is the difference between the hypernucleus mass and its constituents. It is defined by the relation BΛ,i = mA−1 Z + mΛ − mHyp,i where mA−1 Z indicates the mass of the hypernuclear core in its ground state and mΛ the mass of the Λ particle. For the calculations of the nuclear masses the AME2003 table has been used [2]. The BΛ distributions for the targets under study are shown in Fig. 1. The production of an hypernucleus is not the only way a stopped K − can produce a π− in the final state. All possible reactions have been generated and reconstructed by the FINUDA Monte Carlo in order to reproduce the overall background of the hypernuclear signal. The simulations pointed out that among others the in-flight K − decay occurring before the entrance in the target was contributing to the background. The μ− produced by such decay in the vicinity of the target can indeed be reconstructed as a π− and can give an entry in the signal region. After a detailed MC analysis, the processes that were found to contribute effectively as a background were the following: (1) K − n → Λπ− , (2) K − p → Σ− π+ and (3) K − (NN) → Σ− N both followed by the Σ− → nπ− in flight decay and (4) K − in-flight decay. The first reaction, the quasifree Λ production, showed a contribution in the bound region (-BΛ < 0) due to reconstruction errors of the π− momentum. The experimental data have been thus fitted to the sum of the histograms representing the relevant backgrounds, and of Gaussians, for the signal. The ROOT TFractionFitter algorithm has been used [3]. The width of the Gaussians has been left free to scale and resulted in values between 1.65 and 1.95 MeV, depending on the target. The results of the fit are superimposed to

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the experimental data in Fig. 1. The Gaussians distributions, corresponding to the hypernuclear peaks, are also shown. 2.1. Binding energies The mean values of the Gaussians correspond to the binding energy of the formed hypernuclear levels. The absolute scale of the binding energy is known at a level of about 0.2 MeV. This value comes from the calibration of the momentum scale performed using the μ+ momentum distribution in the region of the monochromatic peak at 235.6 MeV/c of the K + → μ+ + νμ decay at rest. The position of the Gaussians could also move of about 0.2-0.3 MeV, when performing the fits and changing the bin size of the distributions, the fit range limits and the cuts applied to obtain the binding energy distribution. This means that, in a first approximation, an overall error of about 0.4 MeV can be attributed to our binding energy measurements. These measurements are summarized here target by target. 7 Li: the binding energy distribution has been fitted with 4 Gaussians, the first 3 corresponding to the 7Λ Li ground state and to 2 excited states, while the 4th may represents the formation of an hyperfragment. We have found the ground state at BΛ = 5.64 ± 0.4 MeV, and the other states at an excitation energy of EX = 1.85 and 3.68 MeV. These latest values are compatible with those inferred from the high-resolution γ spectroscopy [4]. 9 Be: the first two Gaussians of the three used in the fit can be surely attributed to the ground state and to an excited state. The presence of the third peak is arguable, in any case it would correspond to an hyperfragment. According to [4] the 9Λ Be has a doublet excited state around 3 MeV above the ground state, the separation being of about 40 keV, well below our resolution. In our distribution such doublet is seen as a single state at an excitation energy EX of 2.99 MeV with respect to the ground state positioned at BΛ = 6.44 ± 0.4 MeV. 13 C: the binding energy distribution shows five distinctive peaks, the first four being attributable to 13 Λ C and the fifth to the formation of an hyperfragment. The ground state has been found at BΛ = 11.18 ± 0.4 MeV and 3 excited states at EX of 4.94, 8.33 and 11.06 MeV. This last value is in agreement with the γ spectroscopy measurement [5] that reported the presence of a doublet in the region of 10.900 MeV, with a separation energy of about 150 keV. D2 O: only the first two peaks of the binding energy distribution are relative to 16 Λ O, while the others indicate the formation of hyperfragments. The ground state shows a BΛ = 13.25 ± 0.4 MeV, while the excited state has been found at EX = 6.68 MeV, well in agreement with [6], that reports an excited doublet with a separation energy of about 200 keV in the region 6.5-6.7 MeV.

2.2. Capture rates From the number of events in the Gaussians, corresponding to the number of formed hypernuclei, and using detailed MC simulations for the calculation of the experiment efficiencies, a measurement of the formation probability per stopped K− , often called capture rate, could be performed, as previously done by FINUDA for 12 Λ C [1]. A preliminary analysis showed, for the four elements under study, a decreasing capture rate as a function of the atomic mass A. Taking into account all the bound states, an overall formation probability ranging from about 0.15 % for 9 7 16 13 Λ Li to 0.03 % for Λ O, with Λ Be and Λ C values around 0.06 %, have been found. The analysis is under way and more precise results will be soon available.

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Figure 1: Binding energy (−BΛ ) distribution in the bound region for the 7 Li, 9 Be, 13 C and D2 O targets. The insets represent the corresponding π− raw momentum distributions. The crosses stand for the experimental data while the superimposed (red) line is the result of the fit. The contribution of the Gaussians is also represented.

3. Conclusions The hypernuclear formation for the following elements 7 Li, 9 Be, 13 C and D2 O has been studied. Preliminary results about binding energies and formation probability per stopped K− have been presented. While a previous measurement about 16 Λ O has been already reported [7], we remind here that the capture rates for 7 Li, 9 Be, 13 C have never been measured before. References [1] M. Agnello et al., Phys. Lett. B 622 (2005) 35. [2] A.H. Wapstra, G. Audi, and C. Thibault Nucl. Phys. A 729 (2003), 129; G. Audi, A.H. Wapstra, and C. Thibault. Nucl. Phys. A 729 (2003), 337. [3] R. Barlow and C. Beeston, Comp. Phys. Comm. 77 (1993) 219-228. [4] H. Tamura et al., Nucl. Phys. A 754 (2005) 58c. [5] H. Kohri et al., Phys. Rev. C 65 (2002) 034607. [6] M. Ukai et al., Phys. Rev. C 77 (2008) 054315. [7] H. Tamura, R. S. Hayano, H. Outa and T. Yamazaki, Prog. Theor. Phys. Suppl. 117 (1994) 1.